"Baby" would because it would be the object of the preposition "a(b)" or "de," both of which take the ablative. (Not all prepositions take the ablative; some take the accusative and I think there are some that take the dative [unless I'm remembering Greek].)

Ablative can be used to mean1. Place where2. Place from which3. Time at which4. Time within which

But take place where. Ablative is here used with a preposition (except poetry and a few special cases). In atrio, in the atrium. In horto, in the garden. If "in" takes an accusative it means "into, toward, etc". In hortum, into the garden. Place where can also take the accusative. Ad hortum, means in the garden as well. The prepositions clue you in here.

I think it better to divided the ablative into separation and locational (the heart of the ablative is separation)

Note a/ab (the preposition) tends to be used for things that are concrete, like chains, but not abstract, like captivity

2. Cause- "Martyrus mortuus est Christo" The Martyr died for Christ.

3. But, when naming a personal agent rather than an instrument, use ab. "Sum pastus ab Christo", I have been fed by Christ

4. Comparison. I can either say "Sum altior eo" I am higher than he is. He then is in the ablative. But if I use quam (meaning than) then it is similar to English "Sum altior quam is" I am taller than he, with he being in agreement with I. If the first thing being compared were accusative, he would be accusative. But when quam is not used, the ablative is

5. Place from which. Normally this takes a preposition. I am from California. Sum de California. I am leaving California. Exeo ab (or ex, or de) California. All ablative. However with towns, cities, small Islands and domus, rus, and humus (home, country and land) no preposition is used. Exeo domo, I am leaving home.

6. To name a part. Pauci ex militis pugnant. Few of the soldiers fought. This will take ex or de

7. Source (often in genealogies). Can take de, sometimes no preposition

Then the locational8. Place where, but only with in, sub, super. (in, under, over). Roma est in Italia. Rome is in Italy. But note, the locative is used from cities, towns, small islands, domus, rus and humus. So "Sum Romae" I am in Rome. Es domi, You are home. Not Sum Romo, nor Es domo, which would implies direction away from Rome or home. Basically with these exceptions prepositions are not used. Instead ablative means motion away, accusative motion toward, and the locative case (usually is the same as the genitive) means place at, in. For other words the prepositions are used

9. Time when (which usually does not take a preposition, but does in some cases and more frequently in later Latin). Nona hora Christus mortuus est. Christ died at the ninth hour.

10. Time with in which. Tribus horis Christus morietur. Within three hours Christ will die. Generally the plural clues you in, but certain nouns like saeculum (a century), aevum (an age or lifetime) will also work in the singular

Other uses

11. Instumental- Scribo stylo. I write with a pencil. Unlike personal agent, no preposition is used11 b. Deponents. Utor stylo. I use a pen. The reason that this is ablative and not accusative is because of what a deponent is. A deponent is a verb with an active meaning but a passive form, or at least that is what you are told. Really it has a more nuanced history. It is derived from the middle voice, that is a reflexive use. "Lavate" means "Ye (plural) wash" and is active. It could mean wash the car. Or I could specify and say "Lavate se" Se is reflexive, so wash yourselves, but that would be poor latin. "Lavamini" is passive imperative in form, and could mean "be you washed" but would mean by itself "wash yourselves" Utor means I benefit myself, and hence the pen is instrumental. I benefit myself with the pen. Or, Frugor gaudiis aeternae vitae. I enjoy the joys of eternal life.

I don't think prepositional object is it either...it's just ablative. While English would use a prepositional phrase, Latin doesn't have to necessarily. That information is just encoded into the case endings. For exmaple, your sentence could be written as: infanti dulcia abduxi. infanti is a dative of disadvantage with no preposition (a/ab, ex, in, per and the like) in sight.

and then there is a fourth usage - the ablative absolute. there is no preposition involved, instead the past participle used in agreement with a noun/pronoun in the ablative case. the important function to remember is the notion of "absolute," i.e. independent but related. The English equivalent is a nominative absolute: